Fractional-order boundary control of fractional wave equation with delayed boundary measurement using Smith predictor

2004 ◽  
Author(s):  
Jinsong Liang ◽  
M.Q.-H. Meng ◽  
YangQuan Chen ◽  
R. Fullmer
Keyword(s):  
Wave Equation ◽  
Boundary Control ◽  
Fractional Order ◽  
Smith Predictor ◽  
Fractional Wave Equation ◽  
Boundary Measurement

Robustness of Boundary Control of Fractional Wave Equations With Delayed Boundary Measurement Using Fractional Order Controller and the Smith Predictor

2005 ◽  
Author(s):  
Jinsong Liang ◽  
Weiwei Zhang ◽  
YangQuan Chen ◽  
Igor Podlubny
Keyword(s):  
Fractional Order ◽  
Wave Equations ◽  
Small Difference ◽  
Smith Predictor ◽  
Fractional Wave Equation ◽  
Instability Problem ◽  
Boundary Measurement ◽  
Fractional Wave Equations ◽  
Fractional Order Controller ◽  
Better Than

In this paper, we analyze the robustness of the fractional wave equation with a fractional order boundary controller subject to delayed boundary measurement. Conditions are given to guarantee stability when the delay is small. For large delays, the Smith predictor is applied to solve the instability problem and the scheme is proved to be robust against a small difference between the assumed delay and the actual delay. The analysis shows that fractional order controllers are better than integer order controllers in the robustness against delays in the boundary measurement.

The boundary control strategy for a fractional wave equation with external disturbances

2019 ◽  
Vol 121 ◽  
pp. 92-97 ◽  
Author(s):  
Jingfei Jiang ◽  
Juan Luis García Guirao ◽  
Huatao Chen ◽  
Dengqing Cao
Keyword(s):  
Wave Equation ◽  
Boundary Control ◽  
Control Strategy ◽  
External Disturbances ◽  
Fractional Wave Equation

scholarly journals Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ming-Sheng Hu ◽  
Ravi P. Agarwal ◽  
Xiao-Jun Yang
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Series Solution ◽  
Differential Operators ◽  
Fractional Wave Equation ◽  
Local Fractional Calculus ◽  
Vibrating String ◽  
Fractional Differential ◽  
Fractional Differential Operators

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.

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